Abstract
Starting from the linear equations for magneto-elastic coupling, the unit cell problem and the homogenized problem are derived as limits of a two-scale convergence process in a periodic homogenization setting. Exploiting the periodicity of the cell problem and the properties of its Fourier series representation allows for a reformulation as a Lippmann–Schwinger type equation. Iterative algorithms to solve these equations are presented and validated by an analytically solvable test problem.
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Acknowledgements
The author would like to thank his supervisor Bernd Simeon and former colleagues Mané Harutyunyan and Dennis Merkert for their work and support.
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Dietrich, F. (2021). FFT-Based Solution Schemes for the Unit Cell Problem in Periodic Homogenization of Magneto-Elastic Coupling. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_29
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